Neural network to control movement and "home in" on a target
I would go with a NEAT algorithm for this one. Basically, you "breed" the right network that does the best every generation. Then Rinse and repeat. Doesn't require a training datbase. Bots compete and evolve as they go.

For example, this demonstration shows how Neataptic.js teaches a bunch of bots to follow a target:
https://wagenaartje.github.io/neataptic/articles/targetseeking/

Here is more complex problem - a game of Agar.io:
https://wagenaartje.github.io/neataptic/articles/agario/